k-means二维向量版(C#)

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以下代码以最简单的二维向量演示了k-means的处理流程

有一堆二维向量<x₁,y₁>,<x₂,y₂>..<x_n,y_n>,聚成两个类

聚类中心就是类中所有向量的均值<x_m,y_m>, x_m = (x₁+x₂+..+x_n)/2, y_m = (y₁+y₂+..+y_n)/2

每次聚类都重新计算各个向量和聚类中心的距离(用欧氏距离),将各个向量分配到离各自最近的类

然后比较本次的聚类中心是否与上次相等,如果相等,即表示所有类已经平衡,聚类结束.

代码

using System;
using System.Collections.Generic;
using System.Text;
using System.Drawing;

namespace Clustering.Demo
{
    /// <summary>
    /// 利用点坐标(二维向量)来演示k-means算法
    /// </summary>
    class Kmeans
    {
        /// <summary>
        /// 点的坐标数组(coordinates)
        /// </summary>
        private static readonly int[,] coords = new int[,]
        {
        { 0, 0 }, { 1, 0 }, { 0, 1 }, { 1, 1 }, { 2, 1 }, { 1, 2 }, { 2, 2 }, { 3, 2 }, { 6, 6 }, { 7, 6 },
        { 8, 6 }, { 6, 7 }, { 7, 7 }, { 8, 7 }, { 9, 7 }, { 7, 8 }, { 8, 8 }, { 9, 8 }, { 8, 9 }, { 9, 9 },
        //{ 12, 12 }, { 12, 13 }, { 13, 14 }, { 14, 14 }, { 14, 15 }, { 15, 16 }, { 16, 14 }, { 17, 15 }, { 16, 18 }, { 16, 17 },
        };

        /// <summary>
        /// 聚类的数量
        /// </summary>
        private static readonly int k = 2;

        /// <summary>
        ///
        /// </summary>
        public static void Cluster()
        {
            Point[] points = GetPoints(); //获取原始数据点
            PointF[] means = new PointF[k]; //当前的聚类中心
            PointF[] prevMeans = new PointF[k]; //之前的聚类中心
            int[] pointAssigns = new int[points.Length]; //每个点所属的类

            InitMeans(points, k, means); //随机选k个点作为聚类中心
            PrintInit(points, k, means); //打印初始数据

            int iter = 0; //迭代次数(iteration times)
            while (true)
            {
                Classify(points, k, means, pointAssigns); //将每个点与各个聚类中心对比进行归类划分

                int conv = 0; //收敛类数(convergent clusters)
                for (int j = 0; j < k; j++)
                {
                    means[j] = CalcMeans(points, pointAssigns, j); //重新计算聚类中心
                    if (Compare(means[j], prevMeans[j]))
                        conv++;
                    else
                        prevMeans[j] = means[j];
                }
                if (conv == k) //新旧聚类中心一样表示该聚类已收敛至平衡
                {
                    break;
                }

                iter++;
                PrintIter(points, k, means, pointAssigns, iter); //打印迭代数据
            }
        }

        /// <summary>
        /// 初始化点数组(根据自定义坐标)
        /// </summary>
        private static Point[] GetPoints()
        {
            int len = coords.GetLength(0);
            Point[] points = new Point[len];
            for (int i = 0; i < len; i++)
            {
                points[i] = new Point(coords[i, 0], coords[i, 1]);
            }
            return points;
        }

        /// <summary>
        /// 随机选k个点作为聚类中心
        /// </summary>
        private static void InitMeans(Point[] points, int k, PointF[] means)
        {
            Random random = new Random();
            for (int i = 0; i < k; i++)
            {
                means[i] = points[random.Next(points.Length)];
            }
        }

        /// <summary>
        /// 将每个点与各个聚类中心对比进行归类划分
        /// </summary>
        private static void Classify(Point[] points, int k, PointF[] means, int[] pointAssigns)
        {
            for (int i = 0; i < points.Length; i++)
            {
                double minDist = double.MaxValue; //最短距离
                for (int j = 0; j < k; j++)
                {
                    double dist = Distance(points[i], means[j]);
                    if (dist < minDist)
                    {
                        minDist = dist;
                        pointAssigns[i] = j;
                    }
                }
                //Console.WriteLine("{0}归入类{1}", points[i], pointAssigns[i]);
            }
        }

        #region 欧氏距离(Euclidean distance)
        /// <summary>
        /// 计算欧氏距离(勾股定理的多维空间扩展)
        /// </summary>
        /// <remarks>
        /// 勾股定理: x^2 + y^2 = z^2
        /// 欧氏距离: distance = sqrt(x1^2 + x2^2 + ... + xn^2)
        /// 欧氏距离的变换式: x1^2 + x2^2 + ... + xn^2 = distance^2
        ///
        /// 二维空间的两点p1(x1,y1)和p(x2,y2),两点间距离dist=sqrt((x1-x2)^2+(y1-y2)^2)
        /// </remarks>
        private static double Distance(PointF p1, PointF p2)
        {
            double pow2X = Math.Pow(p1.X - p2.X, 2);
            double pow2Y = Math.Pow(p1.Y - p2.Y, 2);
            return Math.Sqrt(pow2X + pow2Y);
        }
        #endregion

        /// <summary>
        /// 计算新的聚类中心(均值)
        /// </summary>
        /// <remarks>
        /// meanX = (x1 + x2 + ... + xn) / n
        /// meanY = (y1 + y2 + ... + yn) / n
        /// </remarks>
        private static PointF CalcMeans(Point[] points, int[] pointAssigns, int j)
        {
            PointF mean = new PointF();
            int n = 0;
            for (int i = 0; i < points.Length; i++)
            {
                if (pointAssigns[i] == j)
                {
                    mean.X += points[i].X;
                    mean.Y += points[i].Y;
                    n++;
                }
            }
            mean.X /= (float)n;
            mean.Y /= (float)n;
            return mean;
        }

        /// <summary>
        /// 比较两个聚类中心是否相等
        /// </summary>
        private static bool Compare(PointF a, PointF b)
        {
            if (((int)(a.X * 10) == (int)(b.X * 10)) && ((int)(a.Y * 10) == (int)(b.Y * 10)))
            {
                return true;
            }
            else
            {
                return false;
            }
        }

        #region 打印数据(print datas)
        /// <summary>
        /// 打印初始数据
        /// </summary>
        private static void PrintInit(Point[] points, int k, PointF[] means)
        {
            Console.WriteLine("总共{0}个样本:", points.Length);
            for (int i = 0; i < points.Length; i++)
            {
                Console.WriteLine("{0}, {1}", points[i].X, points[i].Y);
            }
            Console.WriteLine("\n初始化时随机选取k个样本作为聚类中心:");
            for (int i = 0; i < k; i++)
            {
                Console.WriteLine("聚类{0}的中心: {1}, {2}", i, means[i].X, means[i].Y);
            }
        }

        /// <summary>
        /// 打印迭代数据
        /// </summary>
        private static void PrintIter(Point[] points, int k, PointF[] means, int[] pointAssigns, int iter)
        {
            Console.WriteLine("\n\n--------第{0}次迭代的结果--------", iter);
            for (int j = 0; j < k; j++)
            {
                Console.WriteLine("\n第{0}个类的成员:", j);
                for (int i = 0; i < points.Length; i++)
                {
                    if (pointAssigns[i] == j)
                    {
                        Console.WriteLine("{0}, {1}", points[i].X, points[i].Y);
                    }
                }
                Console.WriteLine("均值(聚类中心): {0}, {1}", means[j].X, means[j].Y);
            }
        }
        #endregion

    }
}